Solve for $x$ and $y$ using elimination. ${-3x-4y = -62}$ ${-5x+3y = -26}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $4$ ${-9x-12y = -186}$ $-20x+12y = -104$ Add the top and bottom equations together. $-29x = -290$ $\dfrac{-29x}{{-29}} = \dfrac{-290}{{-29}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-3x-4y = -62}\thinspace$ to find $y$ ${-3}{(10)}{ - 4y = -62}$ $-30-4y = -62$ $-30{+30} - 4y = -62{+30}$ $-4y = -32$ $\dfrac{-4y}{{-4}} = \dfrac{-32}{{-4}}$ ${y = 8}$ You can also plug ${x = 10}$ into $\thinspace {-5x+3y = -26}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ + 3y = -26}$ ${y = 8}$